where \({S}=\frac{1}{n} \sum _{i=1}^n {x}_i{x}_i^\top \)  is the sample covariance matrix, \(h\)  is a regularization penalty, and \(\lambda \in \mathbb {R}^{+}\)  is a regularization parameter.
The \(\ell _1\) -norm if often used as penalty in order to promote a sparse structure in \({\Theta }\) , which is at the foundation of the well-known \({\rm GLasso}\)  algorithm [1]}, [2]}, [3]}, [4]}.
Many other convex on non-convex penalties have been considered in this stetting [5]}, [6]}, [7]}.
Depending on the assumptions, it can also be beneficial to consider penalties that promote certain types of structured sparsity patterns [8]}, [9]}.
Another main example of structure within the conditional correlations is total positivity, also known as attractive Gaussian graphical models, that assumes \({\Theta }_{q\ell }\le 0,~\forall q \ne \ell \)  [10]}, [11]}.
In attractive Gaussian graphical models, the identifiability of the precision matrix to the graph Laplacian [12]}, has also attracted recent interest from the point of view of graph learning [13]}, [14]}, [15]}.
